List of Errors in Free Lattices

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Page 7, line 6

Change lattice to lattices

Page 11, proof of Lemma 1.3

(Margarita Ramalho) Zorn's lemma should be invoked here. But a direct proof avoiding Choice is not difficult.

Page 8, line 28

"An element in a lattice."

Page 18, line 22

Change "are" to "exists."

Page 71, line 12

The statement about \( J(p) \) should read: \( J(p) \) is the smallest set such that every join cover of an element in \( J(p) \) can be refined to one in \( J(p) \).

Page 98, line 38

In the proof of Lemma 5.6 replace the paragraph that begins "First consider the case ...", with

First note that if \(a \sqsubseteq c\) and \(b \sqsubseteq c\), then, since \(c \in A(a) \cap B(b)\), the special property of \(\sqsubseteq\) gives \(a \sim c \sim b\). Now consider the case when \(a \sqsubseteq b\). If \(b \sqsubseteq c\), then by the above remarks \(a \sim c \sim b\). This implies \(g(a)\) is a joinand of \(g(b)\), and so \(g(a) \le g(b)\). Hence we may assume \(c \sqsubset b\), and thus by induction \(g(a) \le g(c)\). Also \(g(c)\) is a joinand of \(g(b)\) and so \(g(c) \le g(b)\) and hence \(g(a) \le g(b)\).

Page 99, line 29

Change \(\ll\) to \(\leq\)

Page 100, line 16

The reference to Theorem 2.14 should be to Corollary 2.16.

Page 108, Theorem 5.33

The first item should simply read: (1) \( L = D(\mathbf{L})\).

Page 141, Corollary 6.12

Change both occurances of \(\sigma\) to \(\tau\) in this corollary since \(\sigma\) is used for a certain endomorphism of FL(X) in this chapter. Also change the \(\sigma\) on the subscript of y in line 10 to \(\tau\) but leave the three \(\sigma\)'s in the displayed formula above alone.

Page 212, line (3) of the listing

Change P to S.

Page 217, line (7) of the listing

Remove the statement \(T\gets\emptyset\) and place it in between lines (8) and (9) (and renumber the lines).

Page 217, line (14) of the listing

Change the \(\lt\) to \(\gt\).

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